Air New Zealand has lifted its stake in Virgin Australia Holdings to 25.9 per cent, the maximum allowed by the Foreign Investment Review Board, following a series of on-market share purchases.

Before the latest round of purchases, which began in February at 34.55c a share and finished last week at 44c a share, Air NZ had already been the largest shareholder in Virgin with a 24.55 per cent stake.

The biggest single purchase made was a line of 19 million shares last week in the tightly-held stock.

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Singapore Airlines and Etihad Airways hold stakes of 22.17 per cent and 21.24 per cent respectively, while Sir Richard Branson's Virgin Group has a 10 per cent stake. Sir Richard has previously sold shares to Singapore Airlines and Etihad but it remains unclear whether he offered any to Air NZ as part of the latest purchases.

Air NZ will not be able to lift its stake further without applying for fresh approvals from FIRB and the competition regulator and would need to be in compliance with "creeping" provisions that only allow for the purchase of an additional 3 per cent every six months.

Virgin's share price has improved since Qantas Airways last month announced it would freeze capacity in the first three months of the 2015 financial year, leading to speculation that airfares may begin to rise again.

Both Singapore Airlines and Etihad have permission to boost their stakes to 22.9 per cent.